Taylorwas making his first competitive start for the province after his summer move from the Queensland Red's and his injury compounds the back-row injury crisis at the club which has already seen captain John Muldoon, Johnny O'Connor and Andrew Browne sidelined.
The growing injury list has forced head coach Eric Ellwood to look for temporary cover for last season's semi-finalists.
"It's not looking good for Ezra. We are waiting for the results of the scan but, even being optimistic, it looks like he will be out for at least four to six weeks," Elwood told the Irish Times.
"We have made a couple of enquiries, but nothing has come out of those yet.
"Last week we had a problem in the front row, and now we have a dilemma in the back row. Andrew Browne is not yet up to speed with his injury and it is not something we want to rush, so we are looking at a temporary replacement to get us out of a hole."
Connacht face Bayonne at the Sportsground on their return from Italy before a double header against Harelquins on December 12 and 17.